An introduction to the physics and electrochemistry of semiconductors: fundamentals and applications

331 Pages·2016·4.08 MB·English

by  Sharon

An Introduction to the Physics
and Electrochemistry of
Semiconductors
Scrivener Publishing
100 Cummings Center, Suite 541J
Beverly, MA 01915-6106
Publishers at Scrivener
Martin Scrivener ([email protected])
Phillip Carmical ([email protected])
An Introduction
to the Physics and
Electrochemistry of
Semiconductors
Fundamentals and Applications
Maheshwar Sharon
Retd. Professor of Indian Institute of Technology,
Bombay
Copyright © 2016 by Scrivener Publishing LLC. All rights reserved.
Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Beverly,
Massachusetts.
Published simultaneously in Canada.
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Cover design by Russell Richardson
Library of Congr ess Cataloging-in-Publication Data:
ISBN 978-1-119-27433-9
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
Taken from “https://www.google.co.in/webhp?sourceid=chrome-instant&ion=1&espv=
2&ie=UTF-8#q=Bhaskaracharya”
A great mathematician Bhaskaracharya (1114–1183 Before Common Era)
suggested that gravitational forces are responsible to keep the planets, the
sun and the moon in their respective orbits, much before the scientists of
present era realized. He calculated the rotation time taken by the moon to
rotate around the sun as 365.2588 days which is 3.5 min more than what
the modern scientists believe. It was suggested that all stars shining in the
nights are also sun like our sun.
The above paragraph stating the work of Bhaskaracharya is cited because
this book is also about utilizing the energy of the Sun to convert it into
electrical power.
To my two daughters,
for their encouragement and support in writing this book:
Manisha Sharon, PhD, Shinshu University, Japan
Chetna Sharon, PhD, Kyushu University, Japan
Contents
Foreword xv
Preface xvii
1 Our Universe and the Sun 1
1.1 Formation of the Universe 1
1.2 Formation of Stars 2
1.2.1 Formation of Energy in the Sun 3
1.2.2 Description of the Sun 6
1.2.3 Transfer of Solar Rays through the Ozone Layer 6
1.2.4 Transfer of Solar Layers through Other Layers 7
1.2.5 Effect of Position of the Sun vis-à-vis the Earth 8
1.2.6 Distribution of Solar Energy 8
1.2.7 Solar Intensity Calculation 8
1.3 Summary 12
Reference 12
2 Solar Energy and Its Applications 13
2.1 Introduction to a Semiconductor 14
2.2 Formation of a Compound 14
2.2.1 A Classical Approach 14
2.2.2 Why Call It a Band and Not a Level? 15
2.2.3 Quantum Chemistry Approach 17
2.2.3.1 Wave Nature of an Electron in a Fixed
Potential 17
2.2.3.2 Wave Nature of an Electron under a
Periodically Changing Potential 19
2.2.3.3 Bloch’s Solution to the Wave Function of
Electrons under Variable Potentials 20
2.2.3.3 Concept of a Forbidden Gap in a Material 22
ix
x Contents
2.2.4 Band Model to Explain Conductivity in Solids 25
2.2.4.1 Which of the Total Electrons Will Accept
the External Energy for Their Excitation? 26
2.2.4.2 Density of States 28
2.2.4.3 How Do We Find the Numbers of
Electrons in These Bands? 29
2.2.5 Useful Deductions 31
2.2.5.1 Extrinsic Semiconductor 33
2.2.5.2 Role of Dopants in the Semiconductor 36
2.3 Quantum Theory Approach to Explain the
Effect of Doping 37
2.3.1 A Mathematical Approach to Understanding
This Problem 39
2.3.2 Representation of Various Energy Levels in a
Semiconductor 40
2.4 Types of Carriers in a Semiconductor 42
2.4.1 Majority and Minority Carriers 42
2.4.2 Direction of Movement of Carriers
in a Semiconductor 42
2.5 Nature of Band Gaps in Semiconductors 44
2.6 Can the Band Gap of a Semiconductor Be Changed? 45
2.7 S ummary 47
Further Reading 47
3 Theory of Junction Formation 49
3.1 Flow of Carriers across the Junction 49
3.1.1 Why Do Carriers Flow across an Interface
When n- and p-Type Semiconductors Are
Joined Together with No Air Gap? 49
3.1.2 Does the Vacuum Level Remain Unaltered,
and What Is the Significance of Showing a
Bend in the Diagram? 52
3.1.3 Why Do We Draw a Horizontal or Exponential
Line to Represent the Energy Level in the
Semiconductor with a Long Line? 52
3.1.4 What Are the Impacts of Migration of Carriers
toward the Interface? 52
3.2 Representing Energy Levels Graphically 54
3.3 Depth of Charge Separation at the Interface of
n- and p-Type Semiconductors 56
3.4 Nature of Potential at the Interface 56
3.4.1 Does Any Current Flow through the Interface? 56
Contents xi
3.4.2 Effect of Application of External Potential to
the p:n Junction Formed by the Two
Semiconductors 58
3.4.2.1 Flow of Carriers from n-Type to p-Type 59
3.4.2.2 Flow of Carriers from p-Type to n-Type 60
3.4.2.3 Flow of Current due to Holes 60
3.4.2.4 Flow of Current due to Electrons 61
3.4.3 What Would Happen If Negative Potential Were
Applied to a p-Type Semiconductor? 62
3.4.3.1 Flow of Majority Carriers from
p- to n-Type Semiconductors 63
3.4.3.2 Flow of Majority Carriers from
n- to p-Type 63
3.4.3.3 Flow of Minority Carrier from
p- to n-Type Semiconductors 64
3.4.3.3 Flow of Minority Carriers from
n- to p-Type Semiconductors 64
3.5 Expression for Saturation (or Exchange) Current I 67
0
3.5.1 F actors on Which Diffusion
Length Depends 70
3.6 Contact Potential θ 71
3.7 Width of the Space Charge Region 75
3.8 Metal–Schottky Junction 81
3.8.1 Current–Voltage Characteristics for
Metal–Schottky Junctions 84
3.8.2 Saturation Current for Metal–Schottky Junctions 87
3.9 Effect of Light on p:n Junctions 90
3.10 Factors to Be Considered in Illuminating the p:n Junction 94
3.10.1 Grids for Collecting the Charges 95
3.10.2 Ohmic Contact on the Back Side of the Junction 96
3.11 Types of p:n Junctions 97
3.12 A Photoelectrochemical Cell 97
3.13 Summary 100
Further Reading 100
4 Effect of Illumination of a PEC Cell 101
4.1 Effect of Light on the Depletion Layer of the
Semiconductor—Electrolyte Junction 101
4.1.1 Origin of Photopotential 102
4.1.2 Origin of Photocurrent 104
4.2 The Fate of Photogenerated Carriers 105
4.3 Magnitude of the Photocurrent 106
xii Contents
4.4 Gartner Model for Photocurrent 108
4.4.1 Photocurrent due to Photogenerated Carriers
in the Space Charge Region 109
4.4.2 Photocurrent due to Photogenerated Carriers
in the Diffusion Region 109
4.4.3 Application of the Gartner Model 111
4.4.4 When α Is Constant 112
4.4.5 When w Is Kept Constant 115
4.4.6 Lifetime of Carriers and Their Mobility 118
4.5 Carrier Recombination 118
4.5.1 Significance of the Lifetime of Carriers 119
4.5.2 Effect of Recombination Center on the
Magnitude of Photocurrent 120
4.5.3 Origin of Recombination Centers 121
4.6 A Mathematical Treatment for the Lifetime of Carriers 122
4.7 Effect of Illumination on Fermi Level-Quasi
Fermi Level 124
4.8 Solar Cell Performance 130
4.9 Current—Voltage Characteristics of a Solar Cell 135
4.10 The Equivalent Circuit of a Solar Cell 138
4.11 Solar Cell Efficiency 139
4.11.1 Absorption Efficiency α 141
λ
4.11.2 Generation Efficiency g 141
λ
4.11.3 Collection Efficiency C 141
λ
4.11.4 Current Efficiency Q 142
λ
4.11.5 Voltage Factor and Fill Factor 142
4.11.6 Analytical Methods for J-V Characteristics
of a Solar Cell 144
4.11.7 Back Wall Cell 145
4.12 Ohmic Contact 147
4.13 Defects in Solids 148
4.13.1 Bulk Defects 150
4.13.2 Surface Structure 150
4.14 Summary 153
Further Reading 153
References 154
5 Electrochemistry of the Metal–Electrolyte Interface 157
5.1 What Is a Metal? 158
5.2 What Is the Structure of Electrolyte and
Water Molecules in an Aqueous Solution? 158
5.3 What Happens When a Metal Is Immersed in Solution? 160